Problem: Let’s play a card game called Gap.

You have 28 cards labeled with two-digit numbers. The first digit (from 1 to 4) represents the suit of the card, and the second digit (from 1 to 7) represents the value of the card.

First, you shuffle the cards and lay them face up on the table in four rows of seven cards, leaving a space of one card at the extreme left of each row. The following shows an example of initial layout.

<image>

Next, you remove all cards of value 1, and put them in the open space at the left end of the rows: “11” to the top row, “21” to the next, and so on.

Now you have 28 cards and four spaces, called gaps, in four rows and eight columns. You start moving cards from this layout.

<image>

At each move, you choose one of the four gaps and fill it with the successor of the left neighbor of the gap. The successor of a card is the next card in the same suit, when it exists. For instance the successor of “42” is “43”, and “27” has no successor.

In the above layout, you can move “43” to the gap at the right of “42”, or “36” to the gap at the right of “35”. If you move “43”, a new gap is generated to the right of “16”. You cannot move any card to the right of a card of value 7, nor to the right of a gap.

The goal of the game is, by choosing clever moves, to make four ascending sequences of the same suit, as follows.

<image>

Your task is to find the minimum number of moves to reach the goal layout.



Input

The input starts with a line containing the number of initial layouts that follow.

Each layout consists of five lines - a blank line and four lines which represent initial layouts of four rows. Each row has seven two-digit numbers which correspond to the cards.

Output

For each initial layout, produce a line with the minimum number of moves to reach the goal layout. Note that this number should not include the initial four moves of the cards of value 1. If there is no move sequence from the initial layout to the goal layout, produce “-1”.

Example

Input

4

12 13 14 15 16 17 21
22 23 24 25 26 27 31
32 33 34 35 36 37 41
42 43 44 45 46 47 11

26 31 13 44 21 24 42
17 45 23 25 41 36 11
46 34 14 12 37 32 47
16 43 27 35 22 33 15

17 12 16 13 15 14 11
27 22 26 23 25 24 21
37 32 36 33 35 34 31
47 42 46 43 45 44 41

27 14 22 35 32 46 33
13 17 36 24 44 21 15
43 16 45 47 23 11 26
25 37 41 34 42 12 31


Output

0
33
60
-1

Solution (in CPP):

Solution:
// 3:15~
#include <bits/stdc++.h>
using namespace std;

#define dump(n) cout<<"# "<<#n<<'='<<(n)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define peri(i,a,b) for(int i=int(b);i-->int(a);)
#define rep(i,n) repi(i,0,n)
#define per(i,n) peri(i,0,n)
#define all(c) begin(c),end(c)
#define mp make_pair
#define mt make_tuple

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;

const int INF=1e9;
const int MOD=1e9+7;
const double EPS=1e-9;

template<typename T1,typename T2>
ostream& operator<<(ostream& os,const pair<T1,T2>& p){
	return os<<'('<<p.first<<','<<p.second<<')';
}
template<typename T>
ostream& operator<<(ostream& os,const vector<T>& a){
	os<<'[';
	rep(i,a.size()) os<<(i?" ":"")<<a[i];
	return os<<']';
}

struct Board{
	ull data[4];
	Board():data{}{}
	int get(int i,int j){
		return data[i]>>j*8&0xff;
	}
	void set(int i,int j,int x){
		(data[i]&=~(0xffull<<j*8))|=(ull)x<<j*8;
	}
};
bool operator==(const Board& a,const Board& b){
	rep(i,4) if(a.data[i]!=b.data[i]) return false;
	return true;
}
namespace std{
	template<>
	struct hash<Board>{
		size_t operator()(const Board& x)const{
			const char* p=(const char*)&x;
			size_t res=2166136261;
			rep(i,sizeof(x)) (res^=*p++)*=16777619;
			return res;
		}
	};
}

int solve()
{
	Board b0;
	rep(i,4) repi(j,1,8){
		int x; cin>>x;
		if(x%10==1) b0.set(x/10-1,0,x);
		else        b0.set(i,j,x);
	}
	Board bz;
	rep(i,4) rep(j,7) bz.set(i,j,(i+1)*10+j+1);
	
	queue<Board> q; q.push(b0);
	int res=0;
	for(;;res++){
		queue<Board> q2;
		unordered_set<Board> vis;
		while(q.size()){
			Board cur=q.front(); q.pop();
			if(cur==bz) return res;
			if(vis.count(cur)) continue;
			vis.insert(cur);
			
			vector<pii> f(48);
			rep(i,4) rep(j,8) if(cur.get(i,j)) f[cur.get(i,j)]=mp(i,j);
			
			rep(i,4) repi(j,1,8) if(cur.get(i,j)==0){
				int left=cur.get(i,j-1);
				if(left==0 || left%10==7) continue;
				Board next=cur;
				int x=left+1;
				next.set(f[x].first,f[x].second,0);
				next.set(i,j,x);
				q2.push(next);
			}
		}
		if(q2.empty())
			return -1;
		swap(q,q2);
	}
}

int main()
{
	int n; cin>>n;
	rep(_,n) cout<<solve()<<endl;
}